Sounds neat, and it would be easy to do with hobby servo motors if you could relax one of your requirements, either the camera weight or the pipe diameter. I'm guessing your camera isn't going to magically get any lighter, but servo motors that can fit in a 1" pipe aren't very powerful.
There are lots of different ways to go here though, so it's time to answer your question with a bunch of mine:
-Does the motorized pan-tilt mechanism have to fit in a 1" pipe, or just the electronics? After all, the 350 gram camera can't fit in a pipe anyway (or can it?).
-Do you want absolute position control (i.e. turn to 30 degrees from straight ahead and 25 degrees up from horizontal) or just relative position control (i.e. turn left a little and up a little)?
-Do you really need speed control, or just to be able to get where you want it to point?
-What sort of budget are you planning on?
And just out of general curiosity, could you tell us a little more about your project?
If you don't mind having the mechanism outside of the pipe, Servo City makes a nice little pan-tilt module here. Depending on how you decide to go, you can control a couple of servos with a Baby Orangutan (the slightly cheaper B-48 would probably do just fine, but the B-168 gives you lots of room to expand). You'll also need a programmer to go with the microcontroller, but there are some combo deals. You could also use just a simple Micro Serial Servo Controller and a serial radio of some sort, with all the intelligence on the remote control side. Either of these would fit in a 1" diameter pipe.
P.S. If you do use hobby servos and you're willing to settle for direct manual control you can just buy a hobby transmitter/receiver pair like the kind made for high-end RC cars and planes to control the servos with the controller's joystick: